A ray of light coming from the point (1,2) is reflected at a point A on the y-axis and then passes through the point (5,3). What are the co-ordinates of point A?

Dear Student

Here you should take three cases
Case (1) Point is at origin,
Case (2) Point is above origin (0,y) , y>0
Case (3) Point is below origin (0,y), y<0

And for all the three cases find the slopes w.r.t point A, and use the concept that incident angles = reflected angle and find the possible values of y, you will get your Points A.
(Origin will not satisfy the concept)

Thanks, Vijay